Airlines are slashing flights and freezing hiring as they experience a sharp drop in bookings and a rise in cancellations in the face of the spreading coronavirus.

Delta Air Lines said Tuesday that travel demand has fallen so badly in the past week that it expects one-third of seats to be empty this month on flights within the United States — previously the market most immune to virus fallout.

Business travelers are grounded as meetings and conferences are being canceled. Leisure travelers are scared.

Normally airlines try to lure reluctant customers by discounting fares, but that won't work in the face of the COVID-19 outbreak.

“If you are scared of flying, you are probably scared at any price,” said Delta President Glen Hauenstein.

Delta, the world's biggest airline by revenue, said it will cut international flights by 20% to 25% and reduce U.S. flying by 10% to 15%, roughly matching cuts previously announced by United Airlines. CEO Ed Bastian said the airline is “prepared to do more” if the outbreak grows.

The airline is cutting spending, including putting a freeze on hiring, delaying voluntary pension contributions and suspending share buybacks.

American Airlines announced it will cut international flying by 10% this summer and reduce U.S. flying by 7.5% in April. It has delayed training of new pilots and flight attendants.

United said it has arranged $2 billion in additional bank borrowing to preserve financial flexibility — raising liquidity from $6 billion to $8 billion.

The airlines are also evaluating their assets — planes, engines, spare parts and other items — to determine what could be used as collateral for more borrowing, if that is needed.

The demand drop-off that began in Asia picked up steam in the U.S. about two weeks ago, when the virus spread outside Asia, notably to Italy. It has been felt equally among business and leisure travelers.

Hauenstein said demand has fallen more sharply on the West Coast — Washington state and California have suffered larger outbreaks — than on the East Coast. He said younger people have been more willing to keep flying; people over 55 less willing.

The virus appears to be most dangerous among older people. The Associated Press reported this week that the White House overruled a plan by the Centers for Disease Control and Prevention to recommend that older and physically weak Americans be advised not to fly on commercial airlines because of the new virus, according to a federal official.

American's CEO, Doug Parker, said the largest decline has been in tickets within seven days of departure, which are often bought by business travelers.

“That is absolutely driven by U.S. corporations putting in place travel advisories and travel restrictions and canceling travel,” he said. “Once we get to the point where corporate America is ready to travel again, that will come back.”

Airlines have been waiving change fees and touting stepped-up cleaning of airplane cabins to make passengers feel more comfortable about flying.

Delta, United, American and most international carriers have suspended flights to China, where the outbreak began and has infected the most people.

U.S. airline officials have expressed steadfast confidence that they can manage their way through the outbreak.

Airline stocks have been among the hardest hit during the market sell-off of the last few weeks.

Since mid-February, shares of American have lost more than half their value, United's stock has fallen more than 40% and Delta and Southwest Airlines more than 25%. They rallied slightly in trading Tuesday morning.